Coupling arrangements



Ml? 31, 1960 J. s. COOK 2,939,092

COUPLING ARRANGEMENTS May 31, 1960 Filed OCT.. 29, 1954 J. S. COOKCOUPLING ARRANGEMENTS 2 Sheets-Sheet 2 SOURCE 6 ur/L /zAT/oN APP/m4 rus/NvE/VTOR J. .5'. COOK ATTORNEY CoUrLING ARRANGEMENTS John S. Cook, NewProvidence, NJ., assignor to Bell Telephone Laboratories, Incorporated,New York, Nfl., a corporation of New York Filed Got. 29, 1954, Ser. No.465,578

Claims. (Cl. S33- 10) This invention relates to coupled transmissionlines and more particularly relates to arrangements for coupling in adirectional manner a pair of transmission lines.

Directional couplers are known in the radio frequency transmission artas a means for transferring into a branch or auxiliary path for traveltherealong in a preselected direction all or an appreciable portion ofthe wave energy continuing along in a given direction in a main path.From reciprocity considerations, such a coupler wave energy in a pair ofpaths may be combined for travel along a single path in a selecteddirection.

However, it has been characteristic of directional couplers of the priorart that they have all been frequency sensitive to a significant extent.Various configurations have been proposed hitherto which utilize specialdistributions of coupling between the main and auxiliary lines foroperation over increased bandwidths, but these have not represented acomplete solution to the problem. Accordingly, a directional couplerwhich is relatively insensitive to frequency over as wide a band offrequencies as is desired is of manifest utility for use in wide bandtransmission systems.

One object of the present invention is to increase the frequencyresponse which can be achieved in a directional coupler.

The present invention is based on the discovery of a novel couplingprinciple which may be succinctly described here as normal modetapering. The essence of such normal mode tapering involves a gradualchange in the field distribution associated with one of the two normalmodes in a coupler including a pair of lines such that initially the onenormal mode corresponds to a distribution in which all the energy is inone line and eventually the same normal mode corresponds to adistribution in which all the energy is in the other line. The shift inthe held distribution associated with the one normal mode is achieved bya change in the relative phase propagation constants of the two linesalong the coupling region in a prescribed fashion. This principle willbe described in more detail hereinafter.

It is characteristic of the coupled systems in accordance with theinvention that the phase propagation characteristics of the two linesare made to vary with respect to one another over the coupling region.In particular, in embodiments where complete power transfer is soughtbetween two coupled lines, the difference in phase propagation constantsor characteristics of the two lines varies from a negative to a positivevalue over the coupling region. In such embodiments the crossover pointof equal phase propagation characteristics corresponds to the point ofequal division of the power between the two guides. In some embodimentsto be described the phase propagation characteristic, which isfamiliarly designated as is made to vary along both lines over thecoupling region and in opposite directions. In other embodiments to bedescribed remains constant in one line, and varies in the other line.

The invention will be better understood from the nited States Patent O1C Patented May 3i, ieee following more detailed description taken inconjunction with the accompanying drawings in which:

Fig. 1 shows in perspective view of a pair of hollow wave guides coupledto form a coupled system of the kind to which the principles of theinvention are applicable;

Figs. 2, 3, 4 and 5 show in schematic form, as dilferent embodiments ofthe invention, coupled lines in which along the coupling region thephase propagation parameters of the two lines taken separately varies ina prescribed manner;

Fig. 6 is a plot of the phase propagation parameters of a coupled linesystem in accordance with the invention;

Fig. 7 is a plot of the phase propagation parameters of a coupled systemof the kind characteristic of the prior art;

Fig. 8 is a plot illustrating the exchange of energy between the twolines of systems of the kind shown in Figs. 2 through 5; and

Fig. 9 illustrates how the principles of the invention can he applied tothe problem of coupling in and out tance and time and whose peakamplitude is independent of time and the coordinate in the direction ofwave propagation. A system which comprises a pair of transmission lineswhich are tightly coupled so that a sizable fraction of the power in onecan be transferred to the other has four normal mode solutions, twoforward and two backward, of which onlythe former will be of concernhere. In considering such a system the rst and faster normal modecorresponds to the case where the wave excitation in the two guides isin phase, and the second and slower normal mode corresponds to the casewhere the wave excitation in the two guides is out of phase. Anyexcitation can be viewed as a combination of such two modes. It ischaracteristic of these two normal modes that in the cases of principalinterest they have a different phase velocity and so, if both present,can interfere to give standing waves. The various directional couplersof the prior art generally have utilized this interference property toachieve directional selectivity. As such, they ordinarily have involvedcoupling regions whose length was afunction of a quarter of the bestwavelength. As a result of this dependence on an interferencephenomenon, it is characteristic of this type of directional couplingthat it is frequency sensitive. However, it is characteristic ofembodiments in accordance with the invention that they do not depend onsuch an interference phenomenon and so can be relatively insensitive tofrequency.

It is found typical of two coupled transmission lines in which thecoupling and the difference in phase propagation constants of the twolines are uniform with distance over the coupling region that if onenormal mode is started propagating along the line substantially none ofits energy will be transferred to the other mode. Accordingly, if only asingle normal mode were excited in such a system this normal mode wouldpropagate without change, and directivity by interference could not beachieved. However, the held distributions associated with this normalmode would remain constant along the coupling region and no normal modetapering would be possible. On the other hand, it is found that ifeither the difference of the phase propagation parameters or thecoupling varies along the coupling region, there will be a transfer ofenergy between normal modes. Coupling which results in such a transferwill be termed hyper-coupling Inasmuch as in the practice of theinvention it is imporrtant to minimize such energy; exchange betweenmodes, but characteristic to have a variation in` the dierence in thephase propagation parameters of the two lines, this variation is madegradual `and the hyper-coupling weak. Some such variation in thedifference in phasev propagation constants is necessary forY normal modetapering in accordance with the invention whereby the eld distributionassociated with one normal mode varies from an initial condition inwhich all the-wave energy is in oneY line to an end condition in whichall the wave energy is in the other line.

It will now be convenient tof discuss with particular reference tothedrawing specificY embodiments of the invention. t Fig. 1 illustrates inperspective view a coupled system comprising a pair of hollow waveguides of rectangular crsos section which have contiguous or commonnarrow side walls A, 11A. The two wave guides are coupled to one anotherby a coupling aperture 12 which extends through side walls 10A and 11A.In practice this coupling aperture may be either a series of couplingslots extending therealong or an elongated slot with ka grid of wiressubdividing it as shown. The region coextensive with the couplingaperture will be termed the coupling or coupled region of thetwo guides.

Fig. 2 is a schematic representation of a coupled system of hollow waveguides in accordance with the invention in which the phase velocity ineach of the two guides is varied by changes in its transverse dimension.The view depicted corresponds essentially to a top view with the topwalls removed. The system shown provides a complete transfer of powerbetween the two guides although for most wave guide applications powerdivisionother than a complete transfer is of primary interest. The twowave guides 10 and 11 are coupled together in the manner shown in Fig. lby wayof a coupling aperture 12 shown here as the broken portion of theline representing the contiguous side walls 10A and 11A. In accordancewith the principles of the invention, the phase velocity characteristicsand hence the phase propagation characteristics of the two guides aremade appreciably different from one another at point A the start of thecoupling region. In particular, it is found that in the case of uniformcoupling over the coupling region it is advantageous from the standpointof improved directivity to have the phase Velocity characteristics asdifferent as feasible at A. In this embodiment the difference in phasevelocity characteristics is achieved by different transverse dimensionsfor the two guides. As shown, at point A the transverse dimenison ofguide 10 is considerably wider than that of guide 11, resulting there ina lower phase velocity. The phase velocities of the two guides aretapered in opposite directions by appropriate changes in the transversedimensions of the guides with progress along the coupling region frompoint A, and at an intermediate point B along the coupling region thephase velocities are equal. As shown, at point B the 4transversedimensions of the two guides are equal. Point B corresponds to the 3decibel power division point, i.e., at this point the power is equalydivided between the two guides. A 3 decibel coupler can be convenientlyhad merely by discontinuing the coupling between the two lines at thispoint. Similarly, by discontinuing the coupling at other intermediatepoints, a corresponding intermediate power division can be realized.However, as shown, the coupling region extends ytherepast and the phasevelocities continue to change in the same way with further progressalong the coupling region so that at the end point C they are widelydissimilar in a sense opposite to that at point A. As at the startingpoint A, it is advantageous from a standpoint of directivity to have thephase velocity difference at point C as large as feasible. In thisembodiment, the difference in phase propagation parameters will varyalong the coupling region in the manner determined by the linearvariation in the transverse dimensions of the two guides. In practice,it may be advantageous to employ different forms of variation of thisdifference. In particular, it appears preferable in the case of uniformcoupling to employ a variation in the diierence of phase propagationcharacteristics along the length of the coupling region whichcorresponds to a cotangent function of an argument between O and 1rradians at the center frequency of the band of operation.

As indicated above it is important to avoid too sharp changes in thevariations` which might give rise to'hypercoupling. As a result, forcomplete power transfers over a broad band of frequencies, it is foundimportant to have the coupling region quite long, at least severalwavelengths ofthe lowest frequency to be coupled.

It is found that the desired coupling can be achieved more readily ifthe coupling coeicient is varied in an appropriate manner at the sametime as the dijerence in phase propagation parameters of the two guidesis varied. In particular, it is found that `the parameter of interestover the coupling region for normal mode tapering is dz Y where H is thehyper-coupling parameter and (2)-6 (2) H 2 Ic(2)1 where l (z) and ,92(z) are the phase propagation characteristics of the two guides over thecoupling region in the absence of coupling as a function of the distancez along the coupling region, and k(z) is the mutual and selfcouplingcoecient between the two guides. In a copending application Serial No.465,579, tiled October 29, 1954 by A. G. Fox, now United States Patent2,834,944, issued May 13, 1958, there are described coupling systems ofthis kind which utilize both variations in the coupling and in thedifference of phase propagation characteristics.

In the system of Fig. 2, guide 10 is shown excited to produce an outputexcitation in the guide 11. Alternatively, guide 11 may be excited toprovide anY output excitation in guide 10. Moreover, from' reciprocityconsiderations either guide may beV excited for propagation inv eitherdirection.

The manner in which the normal modes are excited can best be describedwith reference to the plots of Fig. 6. In Fig. 6 there is plottedagainst distance along the coupling region the phase propagationcharacteristics of the two forward normal modes associated with a pairof guides coupled as shown in Fig. 2. There is being omitted the lengthymathematical analysis leading to these results. Points A, B and C'alongthe abscissa correspond to points A, B and C of the coupling region ofthe system shown in Fig. 2. The phase propagation characteristics alongthe coupling region can be shown to vary as depicted, the fast normalmode having a phase propagation characteristic f which reaches a maximumat B, the slow mode having a phase propagation characteristic whichreaches a minimum at B. Aty B, the difference between the parameters ,3fand corresponds to twice the coupling coefficient k which Vis a constantin the case under discussion.

It is found characteristic that at A the. fast normal mode hasV a phasepropagation characteristic'f which nearly'matches the phase propagationconstant l of the wave guide 11 with the faster `phase lvelocity whilethe slow normal mode lhas a characteristic which nearly matches thephase propagation constant 182 of wave guide 10. In the plot, to theleft of A there are plotted the phase propagation constants of thetwoguides to the left of the start of the coupling region. The degree ofmismatch is related both to the coupling and the difference in phasepropagation constants of the two guides at A. In arrangements whichemploy uniform coupling, the larger the difference in phase propagationconstants of the two lines the smaller is this mismatch. In arrangementswhich use both variations in coupling and in this difference, themismatch may be eliminated.

It is further found characteristic in the case here described that at Cthe parameters f and s have values nearly equal to those of wave guidewith the fast phase velocity and wave guide 11 with the slow phasevelocity, respectively. This corresponds to a shift in the matchedrelationship. The parameters [if and ,8s are matched to those ofdifferent guides at the two ends of the coupling region. This isconsistent with the shift in field distribution between the two guidesresulting from the normal mode tapering.

For the sake of simplicity guide 10 has been assumed to have a phasepropagation constant at A equal to that of guide 11 at C and vice versa.Of importance is the fact that along the entire coupling region the twonormal modes have different values. This is achieved particularly byhaving the propagation constants of the two guides very different at theboundaries of the coupling region. Hereinafter, with respect to Fig. 7there is compared the phase propagation characteristics of a directionalcoupler of the kind which employs wave guides of substantially equalpropagation constants at the boundaries of the coupling region.

Still with reference to Fig. 6, in operation when a wave is launched inonly one of the two guides at point A, which of the two normal modes isexcited in the coupling region is determined by which of the two guidesis excited. If guide 11 is excited initially corresponding to excitationof the faster mode of the two uncoupled lines, the fast normal mode ofthe coupled system is excited preferentially because of the matchedrelationship in propagation constants therebetween. Alternatively,initial excitation of guide 10 excites the slow normal mode of thecoupled system. To the extent of the degree of mismatch, the othernormal mode is excited. At B, the power in the two guides will either bein-phase or out-of-phase, depending on which of the two normal modes isexcited in the coupling regions. It is characteristic of a coupledsystem of this kind that when only one of the two guides is initiallyexcited, because of the matched relationships plotted in the phasepropagation parameters, only one normal mode is launched to anappreciable extent at the start of the coupling region. As aconsequence, if the hypercoupling between the two normal modes is keptsmall along the coupling region the other normal mode remainssubstantially unexcited.

However, it is found that there is a transfer in energy between the twoguides within the one mode. In particular, the transfer has the formshown in Fig. 8 where the percentage of power in each of the two guidesis plotted against distance along the coupling region. The case depictedrepresents one in which the power was launched initially in guide 11. Itis noted that there are ripples in the power characteristics of eachguide. Such ripples result from the presence of a small amount of theundesired other normal mode resulting from the mismatch at theboundaries. By reducing this mismatch, the amplitude of the ripple canbe reduced. Moreover, although there is not a complete transfer of powerin the case of uniform coupling, the transfer approaches unityasymptotically so that for a suiiiciently long coupling region thetransfer is complete for all practical purposes. If the coupling is alsovaried, complete transfers of power are possible. It will generally bedesirable to terminate the diiferent ends of the Wave guides in theircharacteristic impedances to minimize reflections.

Alternatively, by way of comparison there is shown in Eig. 7 a plot ofthe same form as that of Fig. 6 for directional couplers of the kindcharacteristic of the prior art in which the two guides uncoupled havethe same phase propagation constants over the coupling region. In thisplot, the region between M and N on the abscissa corresponds to thecoupling region which after coupling is characterized by slow and fastforward normal modes of different propagation constants and 'f,respectively. However, in regions before and beyond the coupling regionthe two guides have substantially the same propagation constant whichhas a value intermediate between that of f and 18's. Consequently, eventhough only one of the two guides is excited initially, because both thefast and the slow forward normal modes characteristic of the couplingregion are equally mismatched to the propagation constant a degeneracyexists at the start of the coupling region and both normal modes will beexcited to approximately the same extent. Because such normal modes havedifferent phase propagation parameters, interference therebetweenresults, and although such interference can be used to achievedirectional coupling, such coupling is inherently frequency sensitive.

Various modifications are possible in the basic embodiment shown in Fig.2. First it is possible to achieve the desired variation in ,8(z) alongthe two lines without change in the physical dimensions of the waveguides by insertion of elements which vary either the dielectricconstant or permeability of the wave guide medium. In the coupled systemshown in Fig. 3 along the coupling region 22 there is incorporated inthe guides 20, 21 inserts 23 and 24, respectively, to achieve thispurpose. At A, the dielectric insert member 23 iills a considerableportion of guide 20 while the dielectric insert member 24 fills asmaller portion of the guide 21, whereby the value of the phasepropagation parameter will be there larger in guide 29. At B, thedielectric inserts fill equal portions of the two guides, and at C theguide 21 is iilled more by its insert member 24. The dielectric insertsare tapered along the coupling region to give a desired fvariation inrelative phase propagation characteristics. A taper which resultssubstantially in a cotangent function in the hyper-coupling parameter Halong the coupling region, as described above, is often advantageous.Various other distributions are also feasible. In practice it may beuseful to include beyond the coupling region ytapered extension portions23A and 24A to the corresponding insert members to avoid abruptdiscontinuities in the guides which may be disturbing. In thisembodiment, too, the crossover point B corresponds to the 3 decibelpoint and by discontinuing the coupling there, a 3 decibel couplerresults. Moreover, again either wave guide may be excited at either endfor propagation in either direction although in general losses may beminimized by having the region of high Wave energy level correspond tothe regions of least dielectric insert, as is the case for excitation inthe manner shown.

Moreover, alternatively the insert members 23 and 24 may be of amaterial of high permeability, such as of ferrite, to achieve thedesired variation in propagation constant.

Although in the two embodiments described above, the phase propagationcharacteristics of each of the two lines is varied along the `couplingregion, it is suflicient to vary the phase propagation characteristic ofonly one of the two lines, since it is the change in difference that isof primary significance. In Fig. 4, the guide 30 is of uniform crosssection, and, accordingly, would have a unifor-m phase propagationconstant along the coupling region 32 in the absence of coupling. Guide31, on the other hand, has a transverse dimension which varies from awidth wider than that of guide 30 at lA to a width narrower than that ofguide 30 at C. B is again used to designate the crossover point. As aresult, the difference in the phase propagation character-istics changessign on opposite sides of point B along the coupling region andincreases in absolute value with increasing separation from B.

other line is kept constant.

vguide V41 either of dielectric or permeable material and a uniforminsert member43 in guide 40. To minimize reections, these ,insertmembers are tapered at'their ends Vbeyond Athefcoul'iling,region `42 toavoid sharp discontinuities in the guides. At pointB, the insert members43 and 44 ll equal portionslofthe two guides.

In theembodiments described, the techniques used for achievingvariations in the -phase propagation characteristics of the two lineswill result in accompanying variations in the characteristic impedancesof the two g-uides. In some applications, this may be undesirable. Suchvariations in the characteristic impedancescan lbe avoided. `Forexample, inthe case where the transverse dimen- Y sion of a guide isvaried to achieve achange in phase propagation characteristic, -acompensating change in the height of the'wave guide may be made to keepthe characteristic impedance substantiallyconstant over the couplingregion. Alternatively, by the concurrent use of both dielectric andpermeable insert members, the phase propagation constant of a guide maybe varied without affecting substantially its characteristic impedance.This is possible because although the phase propagation constant of awave guide varies in the same way with changes in either the dielectricconstant or permeability ofthe bounded medium, its characteristicimpedance varies in opposite directions for changes in the dielectricconstant and permeability of the Ibounded medium. Y

Although in each of the embodiments described, the difference in phasepropagation constants is achieved in a continuously taperingcharacteristic -it is obvious that an analogous eiect can be achieved bya series of discrete step variations.

- Moreover, although the embodiments described above have relatedspecifically to a coupled system comprising a pair of hollow'waveguides, lthe principles can be extended to coupled systems comprisingother forms of transmission lines.

In particular, the invention has special application to a coupledYsystem comprising a pair of helical conductors. Helical conductors areassuming great importance as transmission lines in the eld of travelingwave tubes wherein in one important form a helical conductor serves asan interaction circuit for propagating aslow electromagnetic wave pastwhich is projected `an electron beam. One ofthe problems characteristicof the use of a helical conductor in this way has been the Adiiiculty inmaking Wideband reectionless connections thereto for coupling in theinput signal and coupling out the output signal. In Fig. 9 there isshown -a traveling wave tube embodying the' principles of the invention.

In the traveling wave tube 50 shown in Fig. 9, an evacuated envelope 51,for example, of glass or quartz, houses the various tube components. Atopposite ends of the tube, an electronsource, shownY schematically as Ythe cathode 52, and the target electrode 53 define a path Yof electronflow therebetween. rounding the path of electron ilow is a helicalconductor Disposed coaxially sur- 54 which serves Vas the waveinteraction circuit. The twoY ends of the helical conductor preferablyare terminated to be` substantially reectionless, shown schematically byterminating impedances 55 and 56. For simplicity of manufacture, thehelix 54 is wound of a uniform pitch. By suitable lead-in connections(not shown) a D.C. potential is applied to the helix S4 whichaccelerates the electron ilow therepast to a velocity substantially thatof the axial velocity of Ythe electric field. of the wave propagatingthereon, in the manner usual in traveling wave tube operation. It isusually desirable to make some'provision (not shown here) for focusingthe electron beam wave energy, :the inner conductor of the coaxial lineis provided with an extension 59 which is wound'about the tube envelopein coupled relation with the upstream end of helix 54. The extension 59which is a wire conductor is wound coaxially `around the outside of'thetube envelope over a region coextensive with the upstream end of Vthehelix 54. The direction or sense of winding of `the outer helix 59 isadvantageously in a. direction opposite to that of the inner helix 54for enhanced coupling therebetween. In accordance with the principles ofthe invention, by variations in'pitch the'phase propagationcharacteristic of the outer helix 59 is gradually decreased from a valueconsiderably larger to one considerably smaller than that of the innerhelix 54 over the coupling region whereby the input wave is transferredcompletely from lthe outerhelix` to the inner helix for propagationtherealong for interaction with the electron flow. The end of the outerhelix isterminated in its characteristic impedance, shown schematicallyby impedance 60'.A i

At the output or downstream end of the inner helix 54, the wave energyis abstracted therefrom for use by utilization'appar'atus 61 by asimilar'arrangement comprising a coaxial line 62 whose inner conductorincludes an extension 63 which is'formed into a helical conductorcoaxially surrounding the envelope over a region coextensive with thedownstream end of the inner helix. 'The outer helix 63, too, has a pitchvariationgwhich results in a phase propagation characteristic whichvaries from Va value considerably larger to one considerably smallerthan that of the inner helix over the coupling region and Vis terminatedin {its characteristic impedance shown schematically as limpedance 64'.I

Itis, of course, evident from what has been said above `that 4the pitchof either of outer helices 59 and 63 alternatively might have varied toprovide a phase propagation characteristic, which changes from a valuesmaller to a value larger than that of the inner helix S61.A Moreover,the pitch of the inner helix instead of being uniform may be varied solong as there is achieved the desired variation in the phase propagationcharacteristicsv of the inner and outer helices over the couplingregion.

'Moreoven it is to be noted that at the crossover point i where theinner and outer helices have the semeV phase lpropagation constantsubstantially equal amountsV of energy are in the two helices. Travelingwave tubes which utilize as the yinteraction circuitV a pair of inter-Wound helices to which connections are made in accordance withprinciples of the present invention are described in copendingapplication' Serial No. 465,580, led October i 29, 1954 by C. Quate,now, YUnited Statesk Patent 2,823,333, issued February 1-l, 1958.

It is to be understood that the specifici embodiments Y described aremerely illustrative of the general principles of the invention. Variousmodifications may be devised by. one skilled in .the art withoutdeparting from the spirit and scope of the present invention. .Moreoventhe 'principles of the invention may be incorporated in the variousdevices of the art which involve a directional transfer .of powerbetween a pairof separate lines, for example, a circulator,

What is claimed is:

1. A coupled line system comprising lirst and second hollow rectangularwave guides which are in' field coupling relation with one another overacoupling region and characterized in that the width of at least one ofthe v two wave guides varies along the coupling region whereby thediierence 1n phase propagation characteristics of the two guides variestherealong, the Yphase propagation characteristics of the guides beingdiierent at each end of the coupling region, the diierences being ofopposite sign.

2. A coupled line system comprising rst and second hollow rectangularwave guides in ield coupling relation with one another over a couplingregion and dielectric means in at least one of said wave guidesextending along the coupling region for varying the difference in phasepropagation constants of the two lines along the coupling region, vthephase propagation characteristics of the guides `being dilerent at eachend of the coupling region, the diterences being of opposite sign.

3. A coupled line system comprising tirst and second hollow rectangularwave guides in eld coupling relation with one another over a couplingregion and permeable material in at least one of said wave guidesextending along the coupling region for varying 'the diierence in phasepropagation constants of the two lines along the coupling region, thephase propagation characteristics of the guides being different at eachend of the coupling region, the diierences being of opposite sign.

4. A coupled line system comprising iirst and second transmission linesin iield coupling relation with one another and characterized in that atone end of the coupling region the characteristic phase propagationconstant of the two lines is appreciably different, and thehypercoupling parameter varies with distance along the coupling regionsubstantially as a cotangent function.

5. An arrangement for effecting power transfer between a pair of coupledtransmission lines comprising first and second transmission lines infield coupling relation with one another over a region of uniformcoupling and characterized in that the hyper-coupling parameter variesalong the coupling region substantially as a cotangent function.

6. A coupled line system comprising rst and second transmission lines ineld coupling relation with one another over a coupling region andcharacterized in that the diierence in the characteristic phasepropagation constants of the two lines decreases without change in signfrom a signiicant value at one end to substantially at the other end,said coupling region being further characterized by being of uniformcoupling and the hypercoupling parameter varies substantially as acotangent function between 0 and-72E along said region.

7. A coupled line system comprising first and second transmission linesin tield coupling relation with one another over a coupling region andcharacterized in that at one end of the coupling region thecharacteristic phase propagation constants of the two lines arediterent, at least one of said lines having a changing characteristicphase propagation constant in the coupling region such that at anintermediate point of said region the characteristic phase propagationconstants of the two lines are equal and at the other end of thecoupling region they are different, the diierence being of opposite sign10 from the difference of the characteristic phase propagation constantsat said one end.

8. An arrangement for effecting a substantially complete transfer ofenergy from one transmission line to another transmission linecomprising iirst and second transmission lines in field couplingrelation with one another over a coupling region which is long relativeto the wavelength of the wave energy to be transferred and characterizedin that at one end of the coupling region the characteristic phasepropagation constants of the two lines are dilerent, at least one ofsaid lines having a changing phase propagation constant in the couplingregion such that at an intermediate point of said region thecharacteristic phase propagation constants of the two lines are equaland at the other end of the coupling region they are different, thedierence being of opposite sign from the difference of thecharacteristic phase propagation constants at said one end.

9. A coupled line system comprising lirst and second helices concentricwith one another over a coupling region and characterized in that at oneend of the coupling region the characteristic phase propagationconstants of the two helices are different, at least one of said heliceshaving a changing characteristic phase propagation constant in thecoupling region such that at an intermediate point of said region thecharacteristic phase propagation constants of the two lines are equaland at the other end of the coupling region they are diierent, thedifference being of opposite side from the difference of thecharacteristic phase propagation constants at said one end.

10. In a traveling wave tube, means forming a path of electron ow, aninteraction circuit comprising a first helical conductor positionedalong the path of ow for propagating an electromagnetic wave in eldcoupling relation therewith, and means in'energy exchange relation withsaid interaction circuit comprising a second helical conductorpositioned in field coupling relation with said first helical conductorover a coupling region and characterized in that at one end of thecoupling region the phase propagation constants of the two helicalconductors are different, at least one of said helical conducto-rshaving a changing phase propagation constant such that at anintermediate point of said region the characteristic phase propagationconstants of the two lines are equal and at the other end of thecoupling region they are diierent, the diierence being of opposite sidefrom the difference of the characteristic phase propagation constants atsaid one end.

References Cited in the tile of this patent UNITED STATES PATENTS2,588,832 Hansell Mar. l1, 1952 2,659,817 Cutler Nov. 17, 1953 2,679,631Korman May 25, 1954 2,824,257 Branch Feb. 18, 1958 FOREIGN PATENTS1,053,556 France Sept. 30, 1953

